11-1 Lines that Intersect Circles Quiz

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Name: ________________________ Class: ___________________ Date: __________ ID: A

11-1 Lines that Intersect Circles Quiz

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Identify the secant that intersects ñA.

a. BC

→ ←

c. DC

b. l d. DA

____ 2. Find the point of tangency and write the equation of the tangent line at this point.

a. point of tangency: B(3, 0); equation of the tangent line: x=3 b. point of tangency: B(3, 0); equation of the tangent line: y=₃ c. point of tangency: C(2, 0); equation of the tangent line: x+y =3 d. point of tangency: A(0, 0); equation of the tangent line: y=_x+₃

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Name: ________________________ ID: A

2 ____ 3. AB and AC are tangent to ñP. Find AB.

a. AB = 11₂ c. AB = 2

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ID: A

11-1 Lines that Intersect Circles Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: A

A secant is a line that intersects a circle at two points. BC

→ ←

is the secant that intersects ñA.

Feedback A _Correct!

B _{This is a tangent. A secant is a line that intersects the circle at two points.} C _{This is a diameter and a chord. A secant is a line.}

D _{This is a radius. A secant is a line that intersects the circle at two points.}

PTS: 1 DIF: Basic REF: 1ccbefba-4683-11df-9c7d-001185f0d2ea OBJ: 11-1.1 Identifying Lines and Segments That Intersect Circles

LOC: MTH.C.11.03.05.06.002 TOP: 11-1 Lines That Intersect Circles KEY: circle | secant DOK: DOK 2

2. ANS: A

A tangent is a line in the same plane as a circle that intersects it at exactly one point. The point of tangency is the point where the tangent and a circle intersect.

The point of tangency on ñA or ñC is B(3, 0). The tangent line is vertical and passes through point B(3, 0). Its equation is x =3.

B _{The tangent line is a line in the same plane as a circle that intersects it at exactly one}

point.

C _{Find the point where the tangent and a circle intersect.} D _{Find the point where the tangent and a circle intersect.}

PTS: 1 DIF: Average REF: 1cce2b06-4683-11df-9c7d-001185f0d2ea OBJ: 11-1.2 Identifying Tangents of Circles

STA: NY.NYLES.MTH.05.GEO.G.G.50.b | NY.NYLES.MTH.05.GEO.G.G.53.a

LOC: MTH.C.11.03.05.05.002 | MTH.C.11.03.05.05.003 TOP: 11-1 Lines That Intersect Circles KEY: point of tangency | circles DOK: DOK 2

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ID: A

2 3. ANS: A

AB=_AC Theorem: If two segments are tangent to a circle from the same exterior point, then the segments are congruent.

3y+4=11_y _Substitute.

4=8y _{Subtract 3}_y_{from both sides.}

y= 1

2 Divide both sides by 2.

AB=3 1 2 Ê Ë Á Á Á ˆ ¯ ˜ ˜ ˜ +4 _Substitute. AB= 11 2 Simplify. Feedback A _Correct!

B _{Substitute this value for y and solve for segment}_AB_. C _{Check your algebra.}

D _{If two segments are tangent to a circle from the same exterior point, then the segments}

are congruent.

PTS: 1 DIF: Average REF: 1cd0b472-4683-11df-9c7d-001185f0d2ea OBJ: 11-1.4 Using Properties of Tangents

STA: NY.NYLES.MTH.05.GEO.G.G.50.a | NY.NYLES.MTH.05.GEO.G.G.50.b | NY.NYLES.MTH.05.GEO.G.G.53.a LOC: MTH.C.11.03.05.05.005

TOP: 11-1 Lines That Intersect Circles KEY: tangent segments | circles DOK: DOK 2

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Name: ________________________ Class: ___________________ Date: __________ ID: B

11-1 Lines that Intersect Circles Quiz

Multiple Choice

____ 1. AB and AC are tangent to ñ_{P. Find}_AB_.

a. AB = 2 c. AB = 1₂

b. AB = 11₂ d. AB = 10

a. DA c. l

b. BC

→ ←

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Name: ________________________ ID: B

2

a. point of tangency: A(0, 0); equation of the tangent line: y=_x+₃ b. point of tangency: C(2, 0); equation of the tangent line: x+y =3 c. point of tangency: B(3, 0); equation of the tangent line: y=3 d. point of tangency: B(3, 0); equation of the tangent line: x=₃

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ID: B

11-1 Lines that Intersect Circles Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: B

3y+₄=₁₁_y _Substitute.

y= 1

AB=3 1 2 Ê Ë Á Á Á ˆ ¯ ˜ ˜ ˜ +4 _Substitute. AB= 11 2 Simplify. Feedback

A _{Check your algebra.} B _Correct!

C _{Substitute this value for y and solve for segment}_AB_.

D _{If two segments are tangent to a circle from the same exterior point, then the segments}

are congruent.

2. ANS: B

→ ←

Feedback

A _{This is a radius. A secant is a line that intersects the circle at two points.} B _Correct!

C _{This is a tangent. A secant is a line that intersects the circle at two points.} D _{This is a diameter and a chord. A secant is a line.}

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ID: B

2 3. ANS: D

The point of tangency on ñ_A_orñ_C_is_B_{(3, 0)}_._{The tangent line is vertical and passes through point}_B_{(3, 0).}

Its equation is x =_3.

Feedback

A _{Find the point where the tangent and a circle intersect.} B _{Find the point where the tangent and a circle intersect.}

C _{The tangent line is a line in the same plane as a circle that intersects it at exactly one}

point.

D _Correct!

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Name: ________________________ Class: ___________________ Date: __________ ID: C

11-1 Lines that Intersect Circles Quiz

Multiple Choice

a. BC

→ ←

c. DA

b. DC d. l

a. point of tangency: C(2, 0); equation of the tangent line: x+_y =3 b. point of tangency: A(0, 0); equation of the tangent line: y=_x+₃ c. point of tangency: B(3, 0); equation of the tangent line: y=3 d. point of tangency: B(3, 0); equation of the tangent line: x=₃

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Name: ________________________ ID: C

2 ____ 3. AB and AC are tangent to ñP. Find AB.

a. AB = 1₂ c. AB = 2

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ID: C

11-1 Lines that Intersect Circles Quiz

Answer Section

MULTIPLE CHOICE 1. ANS: A

→ ←

B _{This is a diameter and a chord. A secant is a line.}

C _{This is a radius. A secant is a line that intersects the circle at two points.} D _{This is a tangent. A secant is a line that intersects the circle at two points.}

2. ANS: D

The point of tangency on ñA or ñC is B(3, 0). The tangent line is vertical and passes through point B(3, 0). Its equation is x =3.

Feedback

A _{Find the point where the tangent and a circle intersect.} B _{Find the point where the tangent and a circle intersect.}

C _{The tangent line is a line in the same plane as a circle that intersects it at exactly one}

point.

D _Correct!

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ID: C

2 3. ANS: D

3y+4=11_y _Substitute.

y= 1

AB=3 1 2 Ê Ë Á Á Á ˆ ¯ ˜ ˜ ˜ +4 _Substitute. AB= 11 2 Simplify. Feedback

A _{Substitute this value for y and solve for segment}_AB_.

B _{If two segments are tangent to a circle from the same exterior point, then the segments}

are congruent.

C _{Check your algebra.} D _Correct!